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Building Computational Fluency, Grade4
A Math Learning Center Publication
by Allyn Fisher
illustrated by Tyson Smith
Bridges Breakout Units
Building Computational Fluency, Grades 5 & 6
Building Computational Fluency, Grade 3
Building Computational Fluency, Grade 2
Building Computational Fluency, Grade 1
Bridge Design & Construction: Data Collection & Analysis
Bugs Across the Curriculum
Crossing the Pond: A Probability Game
Exploring Money: Adding, Counting, Sorting and Patterning
Exploring Time: Hours, Minutes and Paper Clocks
Frogs Across the Curriculum
Geometry: Pattern Blocks, Polydrons and Paper Quilts (Grade 1)
Geometry: Shapes, Symmetry, Area and Number (Grade 2)
Math Buckets: Sorting and Patterning
Math with a Sock: Probability and Fractions
My Little Farm: Money, Place Value and Mapping
Penguins: Measuring, Sorting, Computation and More
Sea Creatures Across the Curriculum
The Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel. 1 800 575–8130.
© 2007 by The Math Learning Center
All rights reserved.
Prepared for publication on Macintosh Desktop Publishing system.
Printed in the United States of America.
QP739 BOBCF4
P0307
The Math Learning Center grants permission to classroom teachers to reproduce blackline
masters in appropriate quantities for their classroom use.
The Math Learning Center is a nonprofit organization serving the education community.
Our mission is to inspire and enable individuals to discover and develop their mathematical
confidence and ability. We offer innovative and standards-based professional development,
curriculum, materials, and resources to support learning and teaching. To find out more,
visit us at www.mathlearningcenter.org.
ISBN 9781602622074
Building Computational Fluency, Grade 4
Introduction
Building Computational Fluency, Grade 4 Overview
Section 1 Assessments
Section 2 Support Activities
Section 3 Fact Fluency Supplement
1
1
4
5
Section 1 Assessments
Unless otherwise indicated on the blackline, run a class set.
Assessment 1
Conducting Assessment 1
Using Information from Assessment 1
August & September Answer Keys
Assessment 1 page 1 of 5
Assessment 1 page 2 of 5
Assessment 1 page 3 of 5
Assessment 1 page 4 of 5
Assessment 1 page 5 of 5
Base Ten Pieces
Money Value Pieces page 1 of 3
Money Value Pieces page 2 of 3
Money Value Pieces page 3 of 3
Paper Bills
Assessment 1 Class Checklist page 1 of 2
Assessment 1 Class Checklist page 2 of 2
Assessment 2
Conducting Assessment 2
Using Information from Assessment 2
Assessment 2 Answer Key
Assessment 1 page 1 of 4
Assessment 1 page 2 of 4
Assessment 1 page 3 of 4
Assessment 1 page 4 of 4
Assessment 1 Class Checklist
Assessment 3: Quick Facts
Introducing the Quick Facts Routine
Continuing with Quick Facts
Multiplication Table
Multiplication Facts Class Checklist
Quick Facts Tracking Sheet
Quick Facts Worksheet Form A
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27
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Quick Facts Worksheet Form B
Quick Facts Worksheet Form C
Quick Facts Worksheet, 2–6
Quick Facts Worksheet, 4–9
Quick Facts Worksheet, 6–12
Assessment 4
Conducting Assessment 4
Using Information from Assessment 4
Assessment 4 Answer Key
Assessment 4 page 1 of 4
Assessment 4 page 2 of 4
Assessment 4 page 3 of 4
Assessment 4 page 4 of 4
Assessment 4 Class Checklist page 1 of 2
Assessment 4 Class Checklist page 2 of 2
Assessment 5
Conducting Assessment 5
Assessment 5 Answer Key
Assessment 5 page 1 of 4
Assessment 5 page 2 of 4
Assessment 5 page 3 of 4
Assessment 5 page 4 of 4
Assessment 5 Class Checklist page 1 of 3
Assessment 5 Class Checklist page 2 of 3
Assessment 5 Class Checklist page 3 of 3
Assessment 6
Conducting Assessment 6
Assessment 6 Answer Key
Assessment 6 page 1 of 6
Assessment 6 page 2 of 6
Assessment 6 page 3 of 6
Assessment 6 page 4 of 6
Assessment 6 page 5 of 6
Assessment 6 page 6 of 6
Base Ten Grid Paper
Assessment 6 Class Checklist page 1 of 3
Assessment 6 Class Checklist page 2 of 3
Assessment 6 Class Checklist page 3 of 3
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Section 2: Support Activites
Follow copy instructions on blacklines to run as needed.
S
Support Activities Grouped by Skill
S 1.1
Support Activity 1, Spinning Around Subtraction, Instructional Considerations
S 1.2
Support Activity 1, Spinning Around Subtraction, Instructional Considerations (cont.)
S 1.3
S 1.4
S 2.1
S 2.2
S 2.3
S 2.4
S 3.1
S 3.2
S 3.3
S 4.1
S 4.2
S 4.3
S 4.4
S 5.1
S 5.2
S 6.1
S 6.2
S 6.3
S 6.4
S 7.1
S 7.2
S 7.3
S 7.4
S 8.1
S 8.2
Support Activity 1, Spinning Around Subtraction, Instructions
Support Activity 1, Spinning Around Subtraction, Instructions (cont.)
S 1.5 Ten-Strips
S 1.6 Spinning Around Subtraction Record Sheet
S 1.7 Spinning Around Subtraction Spinner
Support Activity 2, More or Less Place Value, Instructional Considerations
Support Activity 2, More or Less Place Value, Instructional Considerations (cont.)
Support Activity 2, More or Less Place Value, Instructions
Support Activity 2, More or Less Place Value, Instructions (cont.)
S 2.5 More or Less Place Value Spinner
S 2.6 More or Less Place Value Record Sheet
S 2.7 Base Ten Pieces
Support Activity 3, Make 100, Instructional Considerations
Support Activity 3, Make 100, Instructions
Support Activity 3, Make 100, Instructions (cont.)
S 3.4 Make 100 Record Sheet
S 3.5 Make 100 Cards: page 1 of 3
S 3.6 Make 100 Cards: page 2 of 3
S 3.7 Make 100 Cards: page 3 of 3
Support Activity 4, Race to 100 & Back, Instructional Considerations
Support Activity 4, Race to 100 & Back, Instructional Considerations (cont.)
Support Activity 4, Race to 100 & Back, Instructions
Support Activity 4, Race to 100 & Back, Instructions (cont.)
S 4.5 Race to 100 & Back Spinner
Support Activity 5, Count Down 400, Instructional Considerations
Support Activity 5, Count Down 400, Instructions
S 5.3 Count Down 400 Record Sheet
S 5.4 Count Down 400 Spinner
Support Activity 6, More or Less Addition, Instructional Considerations
Support Activity 6, More or Less Addition, Instructional Considerations (cont.)
Support Activity 6, More or Less Addition, Instructions
Support Activity 6, More or Less Addition, Instructions (cont.)
S 6.5 More or Less Addition Record Sheet
S 6.6 More or Less Addition/Subtraction Spinner 1
S 6.7 More or Less Addition/Subtraction Spinner 2
Support Activity 7, More or Less Subtraction, Instructional Considerations
Support Activity 7, More or Less Subtraction, Instructional Considerations (cont.)
Support Activity 7, More or Less Subtraction, Instructions
Support Activity 7, More or Less Subtraction, Instructions (cont.)
S 7.5 More or Less Subtraction Record Sheet
Support Activity 8, Three Turns to Win, Instructional Considerations
Support Activity 8, Three Turns to Win, Instructions
S 8.3 Three Turns to Win Game Board
S 8.4 Three Turns to Win Record Sheet
S 8.5 Small Number Charts
S 9.1 Support Activity 9, Finish with $10, Instructional Considerations
S 9.2 Support Activity 9, Finish with $10, Instructions
S 9.3 Finish with $10 Game Board: page 1 of 2
S 9.4 Finish with $10 Game Board: page 2 of 2
S 9.5 Money Value Pieces: page 1 of 3
S 9.6 Money Value Pieces: page 2 of 3
S 9.7 Money Value Pieces: page 3 of 3
S 10.1 Support Activity 10, An Hour or Bust to the Minute, Instructional Considerations
S 10.2 Support Activity 10, An Hour or Bust to the Minute, Instructions
S 10.3 An Hour or Bust to the Minute Record Sheet
S 11.1 Support Activity 11, Get Me to the Bus on Time, Instructional Considerations
S 11.2 Support Activity 11, Get Me to the Bus on Time, Instructional Considerations (cont.)
S 11.3 Support Activity 11, Get Me to the Bus on Time, Instructions
S 11.4 Get Me to the Bus on Time Game Board: page 1 of 2
S 11.5 Get Me to the Bus on Time Game Board: page 2 of 2
S 11. 6 Get Me to the Bus on Time Record Sheet
S 12.1 Support Activity 12, Spinning Around Multiplication, Instructional Considerations
S 12.2 Support Activity 12, Spinning Around Multiplication, Instructional Considerations (cont.)
S 12.3 Support Activity 12, Spinning Around Multiplication, Instructions
S 12.4 Spinning Around Multiplication Spinner
S 12.5 Spinning Around Multiplication Record Sheet
S 12.6 Grid Paper
S 13.1 Support Activity 13, Array Challenge, Instructional Considerations
S 13.2 Support Activity 13, Array Challenge, Instructions
S 13.3 Array Challenge Cards: page 1 of 3
S 13.4 Array Challenge Cards: page 2 of 3
S 13.5 Array Challenge Cards: page 3 of 3
S 14.1 Support Activity 14, Multiplication Challenge, Instructional Considerations
S 14.2 Support Activity 14, Multiplication Challenge, Instructional Considerations (cont.)
S 14.3 Multiplication Challenge Cards: page 1
S 14.4 Multiplication Challenge Cards: page 2
S 14.5 Multiplication Challenge Cards: page 3
S 15.1 Support Activity 15, Spinning for Arrays, Instructional Considerations
S 15.2 Support Activity 15, Spinning for Arrays, Instructions
S 15.3 Spinning for Arrays Spinner
S 15.4 Array Cards: page 1
S 15.5 Array Cards: page 2
S 15.6 Array Cards: page 3
S 15.7 Array Cards: page 4
S 16.1 Support Activity 16, Product Bingo, Instructional Considerations
S 16.2 Support Activity 16, Product Bingo, Instructions
S 16.3 Product Bingo Boards
S 16.4 Product Bingo Spinner
S 17.1 Support Activity 17, What’s Missing? Bingo, Instructional Considerations
S 17.2 Support Activity 17, What’s Missing? Bingo, Instructions
S 17.3 What’s Missing? Bingo Boards
S 17.4 What’s Missing? Bingo Cards: page 1 of 4
S 17.5 What’s Missing? Bingo Cards: page 2 of 4
S 17.6 What’s Missing? Bingo Cards: page 3 of 4
S 17.7 What’s Missing? Bingo Cards: page 4 of 4
S 17.8 Grid Paper
S 18.1 Support Activity 18, More or Less Addition Big Time, Instructional Considerations
S 18.2 Support Activity 18, More or Less Addition Big Time, Instructions
S 18.3 Support Activity 18, More or Less Addition Big Time, Instructions (cont.)
S 18.4 More or Less Addition Big Time Record Sheet
S 18.5 More or Less Addition/Subtraction Big Time Spinner 1
S 18.6 More or Less Addition/Subtraction Big Time Spinner 2
S 19.1 Support Activity 19, More or Less Subtraction Big Time, Instructional Considerations
S 19.2 Support Activity 19, More or Less Subtraction Big Time, Instructional Considerations (cont.)
S 19.3 Support Activity 19, More or Less Subtraction Big Time, Instructions
S 19.4 More or Less Subtraction Big Time Record Sheet
S 20.1 Support Activity 20, Larger Numbers on a Line, Instructional Considerations
S 20.2 Support Activity 20, Larger Numbers on a Line, Instructions
S 20.3 Larger Numbers on a Line Problem Cards
S 20.4 Larger Numbers on a Line Record Sheet
S 21.1 Support Activity 21, Perimeter Showdown, Instructional Considerations
S 21.2 Support Activity 21, Perimeter Showdown, Instructions
S 21.3 Perimeter Cards
S 21.4 Perimeter Showdown Record Sheet
S 21.5 Grid Paper
S 22.1 Support Activity 22, Spin & Multiply, Instructional Considerations
S 22.2 Support Activity 22, Spin & Multiply, Instructions
S 22.3 Spin & Multiply Spinner
S 22.4 Spin & Multiply Record Sheet
S 23.1 Support Activity 23, Remainders Win, Instructional Considerations
S 23.2 Support Activity 23, Remainders Win, Instructions
S 23.3 Support Activity 23, Remainders Win, Instructions (cont.)
S 23.4 Divisor Spinner
S 23.5 Remainders Win Record Sheet
S 23.6 Number Charts
S 24.1 Support Activity 24, Fraction Race, Instructional Considerations
S 24.2 Support Activity 24, Fraction Race, Instructions
S 24.3 Support Activity 24, Fraction Race, Instructions (cont.)
S 24.4 Eighths Strips
S 24.5 Eighths Spinner
S 24.6 Twelfths Strips
S 24.7 Twelfths Spinner
S 25.1 Support Activity 25, Fraction Bingo, Instructional Considerations
S 25.2 Support Activity 25, Fraction Bingo, Instructions
S 25.3 Fraction Bingo Boards
S 25.4 Fraction Bingo Cards: page 1 of 3
S 25.5 Fraction Bingo Cards: page 2 of 3
S 25.6 Fraction Bingo Cards: page 3 of 3
S 26.1 Support Activity 26, Round & Add Tens, Instructional Considerations
S 26.2 Support Activity 26, Round & Add Tens, Instructions
S 26.3 Support Activity 26, Round & Add Tens, Instructions (cont.)
S 26.4 Round & Add Tens Spinner
S 26.5 Round & Add Tens Record Sheet
S 27.1 Support Activity 27, Round & Add Hundreds, Instructional Considerations
S 27.2 Support Activity 27, Round & Add Hundreds, Instructions
S 27.3 Support Activity 27, Round & Add Hundreds, Instructions (cont.)
S 27.4 Round & Add Hundreds Spinner
S 27.5 Round & Add Hundreds Record Sheet
S 28.1 Support Activity 28, Divide ’Em Up, Instructional Considerations
S 28.2 Support Activity 28, Divide ’Em Up, Instructions
S 28.3 Divide ’Em Up Spinner
S 28.4 Divide ’Em Up Record Sheet
S 29.1 Support Activity 29, Money, Fraction & Decimal Showdown, Instructional Considerations
S 29.2 Support Activity 29, Money, Fraction & Decimal Showdown, Instructions
S 29.3 Money, Fraction & Decimal Showdown Cards: page 1 of 5
S 29.4 Money, Fraction & Decimal Showdown Cards: page 2 of 5
S 29.5 Money, Fraction & Decimal Showdown Cards: page 3 of 5
S 29.6 Money, Fraction & Decimal Showdown Cards: page 4 of 5
S 29.7 Money, Fraction & Decimal Showdown Cards: page 5 of 5
Section 3 Fact Fluency Supplement
Follow copy instructions on blacklines to run as needed.
F
F1
Fact Fluency Supplement: Multiplication and Division
Fact Fluency with 2’s: Multiplying & Dividing by 2
F2
F3
F4
F5
F6
F7
F8
F9
F 10
F 11
F 12
Fact Fluency with 2’s: Practice Multiplying by 2 & 10
Fact Fluency with 2’s: Division Capture 2’s & 10’s
Fact Fluency with 2’s: Flashcard Bingo 2’s
Fact Fluency with 2’s: Flashcards, page 1 of 2
Fact Fluency with 2’s: Flashcards, page 2 of 2
Fact Fluency with 3’s: Multiplying & Dividing by 3
Fact Fluency with 3’s: Practice Multiplying by 3 & 2
Fact Fluency with 3’s: Division Capture 3’s & 2’s
Fact Fluency with 3’s: Flashcard Bingo 3’s
Fact Fluency with 3’s: Flashcards, page 1 of 2
Fact Fluency with 3’s: Flashcards, page 2 of 2
F 13
F 14
F 15
F 16
F 17
F 18
F 19
F 20
F 21
F 22
F 23
F 24
F 25
F 26
F 27
F 28
F 29
F 30
F 31
F 32
F 33
F 34
F 35
F 36
F 37
F 38
F 39
F 40
F 41
F 42
F 43
F 44
F 45
F 46
F 47
F 48
F 49
F 50
F 51
F 52
F 53
F 54
F 55
F 56
F 57
Fact Fluency with 4’s: Multiplying & Dividing by 4
Fact Fluency with 4’s: Practice Mulitplying by 4 & 2
Fact Fluency with 4’s: Division Capture 4’s & 2’s
Fact Fluency with 4’s: Flashcard Bingo 4’s
Fact Fluency with 4’s: Flashcards, page 1 of 2
Fact Fluency with 4’s: Flashcards, page 2 of 2
Fact Fluency with 5’s: Multiplying & Dividing by 5
Fact Fluency with 5’s: Practice Multiplying by 5 & 10
Fact Fluency with 5’s: Division Capture 5’s & 10’s
Fact Fluency with 5’s: Flashcard Bingo 5’s
Fact Fluency with 5’s: Flashcards, page 1 of 2
Fact Fluency with 5’s: Flashcards, page 2 of 2
Fact Fluency with 6’s: Multiplying & Dividing by 6
Fact Fluency with 6’s: Practice Multiplying by 6 & 5
Fact Fluency with 6’s: Division Capture 6’s & 5’s
Fact Fluency with 6’s: Flashcard Bingo 6’s
Fact Fluency with 6’s: Flashcards, page 1 of 2
Fact Fluency with 6’s: Flashcards, page 2 of 2
Fact Fluency with 7’s: Multiplying & Dividing by 7
Fact Fluency with 7’s: Practice Multiplying by 7 & 8
Fact Fluency with 7’s: Missing Number Capture 7’s & 8’s
Fact Fluency with 7’s: Flashcard Bingo 7’s
Fact Fluency with 7’s: Flashcards, page 1 of 2
Fact Fluency with 7’s: Flashcards, page 2 of 2
Fact Fluency with 8’s: Multiplying & Dividing by 8
Fact Fluency with 8’s: Practice Multiplying by 8 & 4
Fact Fluency with 8’s: Missing Number Capture 8’s & 4’s
Fact Fluency with 8’s: Flashcard Bingo 8’s
Fact Fluency with 8’s: Flashcards, page 1 of 2
Fact Fluency with 8’s: Flashcards, page 2 of 2
Fact Fluency with 9’s: Multiplying & Dividing by 9
Fact Fluency with 9’s: Practice Multiplying by 9 & 3
Fact Fluency with 9’s: Missing Number Capture 9’s & 3’s
Fact Fluency with 9’s: Flashcard Bingo 9’s
Fact Fluency with 9’s: Flashcards, page 1 of 2
Fact Fluency with 9’s: Flashcards, page 2 of 2
Fact Fluency with 10’s: Multiplying & Dividing by 10
Fact Fluency with 10’s: Practice Multiplying by 10 & 5
Fact Fluency with 10’s: Missing Number Capture 10’s & 5’s
Fact Fluency with 10’s: Flashcard Bingo 10’s
Fact Fluency with 10’s: Flashcards, page 1 of 2
Fact Fluency with 10’s: Flashcards, page 2 of 2
Fact Fluency with 11’s: Multiplying & Dividing by 11
Fact Fluency with 11’s: Practice Multiplying by 11 & 10
Fact Fluency with 11’s: Missing Number Capture 11’s & 10’s
F 58
F 59
F 60
F 61
F 62
F 63
F 64
F 65
F 66
F 67
F 68
F 69
F 70
F 71
F 72
F 73
F 74
F 75
F 76
F 77
F 78
F 79
F 80
F 81
Fact Fluency with 11’s: Flashcard Bingo 11’s
Fact Fluency with 11’s: Flashcards, page 1 of 2
Fact Fluency with 11’s: Flashcards, page 2 of 2
Fact Fluency with 12’s: Multiplying & Dividing by 12
Fact Fluency with 12’s: Practice Multiplying by 12 & 10
Fact Fluency with 12’s: Missing Number Capture 12’s & 10’s
Fact Fluency with 12’s: Flashcard Bingo 12’s
Fact Fluency with 12’s: Flashcards, page 1 of 2
Fact Fluency with 12’s: Flashcards, page 2 of 2
Fact Fluency with 2’s–6’s: Mixed Facts
Fact Fluency with 2’s–6’s: Secret Path Problems, Set 1
Fact Fluency with 2’s–6’s: Secret Path Problems, Set 2
Fact Fluency with 2’s–6’s: Division Capture
Fact Fluency with 4’s–9’s: Mixed Facts
Fact Fluency with 4’s–9’s: Secret Path Problems, Set 1
Fact Fluency with 4’s–9’s: Secret Path Problems, Set 2
Fact Fluency with 4’s–9’s: Division Capture
Fact Fluency with 6’s–12’s: Mixed Facts
Fact Fluency with 6’s–12’s: Secret Path Problems, Set 1
Fact Fluency with 6’s–12’s: Secret Path Problems, Set 2
Fact Fluency with 6’s–12’s: Division Capture
Fact Fluency Secret Path Answer Keys
Fact Fluency Secret Path Answer Keys (cont.)
Fact Fluency Secret Path Answer Keys (cont.)
Building Computational Fluency,
Grade 4 Overview
Building Computational Fluency, Grade 4 is a supplement designed to provide
you with powerful and flexible tools to assess and support students in developing key computational skills and concepts. Organized into three sections,
this supplement enables you to assess some or all of your students on computational skills throughout the school year and provide support to students
who need extra help in key areas, including:
• place value understandings
• rounding
• multiplication and division facts through 12’s
• multi-digit addition and subtraction
• multi-digit multiplication and division
• fraction and decimal sense
• adding and subtracting fractions and decimals
In Section 1, you’ll find a set of assessments designed to be administered at
key points throughout the school year. These assessments serve as a useful complement to any fourth grade math program. They also provide tools
to check students’ proficiency with basic multiplication and division facts
on a regular basis. In Section 2, you’ll find a collection of Support Activities
designed to help students who indicate needs in the specific areas assessed.
The games in this section are based around visual models and strategies, and
help students develop deep conceptual understandings as well as proficiency.
They can be used as instructional resources with your entire group, or as
tools to remediate targeted students. Section 3 is a Fact Fluency Supplement
that provides the kind of systematic, strategy-based practice students need to
master basic multiplication and division facts. The worksheets and practice
games in this section are designed to be tailored to the needs of individuals,
and can be used with selected students or with your entire class. Each section is described in more detail below.
Section 1 Assessments
The six assessments in this collection are designed to help you gauge how
your students are doing with key computational skills throughout the year.
Assessment 1 is intended for use during the first few weeks of school. Depending on your district expectations, this assessment may be useful in determining whether your incoming fourth graders are working at, above, or
below grade level.
Bridges Breakouts • 1
Grade 4
Building Computational Fluency
Building Computational Fluency Blackline
Building Computational Fluency Blackline
NAME
DATE
NAME
Assessment 1 page 1 of 5
Assessment 1 page 3 of 5
1
Show all your work and explain your thinking for problems 4, 5, 6, and 7.
2
Solve these addition problems.
6
+6
____
6
+9
____
6
+7
____
8
+8
____
9
+7
____
9
+5
____
8
+3
____
8
+9
____
7
+3
____
8
+6
____
8
+4
____
7
+8
____
7
+7
____
4
+6
____
9
+
10
____
5
+7
____
8
+5
____
9
+9
____
9
+3
____
4
+7
____
NAME
16
–8
____
15
–8
____
DATE
11
–8
____
4
123
+ 88
_____
5
$3.69 + $1.23 =
6
304
– 187
_____
7
$5.00 – $3.72 =
Solve these subtraction problems.
14
–7
____
14
– 10
____
Building Computational Fluency Blackline
15
– 10
____
14
–8
____
8
In the spaces below, write the following numbers in order from least to
greatest.
Assessment 1 page 2 of 5
3
DATE
14
13
12
Solve____
these
problems.
– 9 multiplication
–3
–8
____
____
6
×1
____
13
–5
____
1
×4
____
17
–9
____
5
×1
____
15
–6
____
16
–9
____
2
×2
____
13
–8
____
13
–7
____
4
×1
____
15
–9
____
19
–9
____
1
×1
____
2,045
18
– 10
____
5
×0
____
123
least
254
1,023
greatest
12
–7
____
1
×5
____
2
×0
____
3
×2
____
2
×4
____
3
×3
____
5
×6
____
6
×2
____
5
×2
____
4
×6
____
3
×6
____
4
×2
____
3
×1
____
2
×5
____
4
×5
____
1
×6
____
1
×2
____
5
×3
____
4
×3
____
5
×4
____
6
×6
____
8
×4
____
3
×4
____
2
×6
____
3
×0
____
1
×3
____
6
×5
____
The first 3 pages of Assessment 1
Even
if many
of2 your students perform very well on Assessment 1, you may
3
6
×5
×3
×3
____
____
____
find that some of them need more practice with multiplication and division facts. Toward that end, another assessment (Assessment 3: Quick Facts)
4
6
2
which
allows
students
to choose their own learning targets and track their
×4
×4
×1
____
____
____
own progress toward fact mastery has been included in the set. Teachers
often
introduce the “Quick Facts” assessment sometime in the fall or early
5
×5
____
winter and continue to administer it weekly or even twice a week until the
majority of their students are fluent with multiplication and division facts.
An extensive set of worksheets and games is featured in the third section of
Building Computational Fluency to provide the systematic practice students
will need to progress through and eventually test out of Assessment 3.
Assessments 2, 4, 5, and 6 are quarterly checkups designed for use at the end
of each grading period to support teachers in conferencing with parents and
reporting on students’ progress. Each of these assessments offers another
look at students’ proficiency with basic facts and host of other key math skills
typically taught in the fall, winter, and early as well as late spring of the
fourth grade year.
All the assessments described above include instructions to the teacher, answer keys, assessment blacklines, and class checklists. Although use of the
2 • Bridges Breakouts
Grade 4
Building Computational Fluency
class checklists is optional, they allow teachers to easily spot strengths and
weaknesses in individual students and in the class as a whole.
mes
t Na
Stud
en
1 & 2 completes 24 out of 40 addition and
subtraction facts in 2 minutes
3 completes 24 out of 40 multiplication
facts in 2 minutes
4a adds with regrouping
4b shows work
5a adds money amounts with regrouping
5b shows work
6a subtracts with regrouping
6b shows work
7a subtracts money amounts with regrouping
7b shows work
8 orders multi-digit numbers
9a multiplies 14 × 6
Building Computational Fluency Blackline Run enough copies to record the results for all students in your class.
A s s e s s m e n t 1 C l a s s C h e c k l i s t p a g e 1 of 2
9b shows work
10a multiplies 200 × 5
10b shows work
11a divides 24 ÷ 6
11b shows work
s
ame
ent
N
Stud
12a divides 13 ÷ 4
12b shows work
13 identifies area model for 1⁄3
14 identifies fraction equivalent to 1⁄3
15 counts money accurately
16 does a multi-step money story problem
17 calculates elapsed time
18 tells time to the minute
Building Computational Fluency Blackline Run enough copies to record the results for all students in your class.
A s s e s s m e n t 1 C l a s s C h e c k l i s t p a g e 2 of 2
Bridges Breakouts • 3
Grade 4
Building Computational Fluency
Section 2 Support Activities
In the second section of this packet, you’ll find a set of 29 partner or small
group games specifically designed to support the skills tested in the assessments described above. These games provide engaging practice with skills including basic multiplication and division concepts and strategies, multi-digit
computation (addition, subtraction, multiplication, and division), rounding,
money, time, decimals, and fractions. Most of these games are based around
visual models such as base ten pieces and arrays, and are intended to help
students develop conceptual understanding as well as proficiency.
Building Computational Fluency Blackline S 25.2
Building Computational Fluency Blackline S 25.3 Run 1 copy for each player.
Fraction Bingo Boards
H Fraction Bingo Boards (Blackline S 25.3, 1 copy for each player)
H Fraction Bingo Cards, pages 1–3 (Blacklines NC S 25.4–25.6, 1 copy cut apart and stored in
an envelope or resealable plastic bag for each pair or small group of players)
2
6
2
4
3
4
1
3
H game markers (Use coins or small objects if you do not have game markers.)
Mix up the Fraction Bingo Cards
and place them face down in a pile.
3
Let one player draw a card. Talk
to each other about what fraction is
shown on the card. How would it be
shown in numerical form on your
bingo boards?
4
Blackline NC S 25.3 Run 1 copy for each player.
Fraction Bingo Boards
Board B
Board A
3
8
1
2
4
6
2
4
1
4
1
3
2
6
2
4
1
6
3
4
2
6
1
8
3
4
1
3
1
8
2
3
1
6
3
8
, and store in
2
4
an envelope for
each pair or grou
1
4
1
3
p of players.
1
6
3
4
2
6
1
8
1
8
2
3
1
6
3
8
Board D
Board C
1
4
4
6
3
8
1
3
1
3
2
4
3
4
2
6
1
8
1
6
1
2
1
8
Blackline NC
S 25.5 Fract
ion Bingo Car
d
Look for that fraction on your board
and cover it with a game marker if you
have it on your board. Each board is
missing some fractions, but if you find
a fraction on your board that is equal to
the fraction on the card, you can put a
game marker on it. You can only cover
one fraction for each card, though.
Take turns drawing cards until one
of you has 3 game markers in a row
horizontally, vertically, or diagonally.
Decide if you want to keep playing
until everyone wins or if you want to
start a new game.
Blackline NC
S 25.5 Fract
ion Bingo Car
d
2
5
Blackline NC
S 25.5 Fract
ion Bingo Car
d
Instructions for Fraction Bingo
Blackline NC
S 25.5 Fract
ion Bingo Car
d
Fraction Bing
o Ca rds page
2 of 3
H Instructions for Fraction Bingo (Blackline S 25.2)
Each player chooses a different
Fraction Bingo Board and gets 9 game
markers.
4
6
apar t along lines
Blackline NC
S 25.5 Fract
ion Bingo Car
d
1
2
1
4
3
4
2
4
2
3
Blackline NC
S 25.5 Fract
ion Bingo Car
d
3
8
al Flue ncy Blac
kline S 25.5
Run 1 copy, cut
Blackline NC
S 25.5 Fract
ion Bingo Car
d
Build ing Com
puta tion
You’ll need
1
Board B
Board A
SUPPORT ACTIVITY
Fraction Bingo
3
8
1
6
Blackline NC
S 25.5 Fract
ion Bingo Car
d
Support Activity 25
Excerpts from Support Activity 25, Fraction Bingo
Although the Support Activities have been designed to complement the assessments in this packet, you can use them as a set of additional instruction
resources for your classroom even if you choose not to conduct the assessments. The activities can be used by educational assistants, parent volun4 • Bridges Breakouts
Grade 4
Building Computational Fluency
teers, resource or title teachers, as well as classroom teachers, and many of
them also make effective homework assignments.
Each activity includes:
• instructional considerations
• playing instructions
• blacklines for game components if needed (spinners, gameboards,
and/or cards)
• record sheet blacklines if needed
Section 3 Fact Fluency Supplement
The Fact Fluency Supplement is designed to be used in conjunction with
the third assessment described above (Assessment 3: Quick Facts), but also
stands alone as systematic and dynamic set of practice sheets for fourth graders who haven’t yet mastered their multiplication and division facts. This
82-page supplement includes worksheets, games, and flashcards for each multiplier from 2 to 12, as well as three different ranges of facts: 2–6, 4–9, and
6–12. Based around such fact strategies as doubles (2’s), double-doubles (4’s),
and half decade facts (5’s) these activities build on one another and provide
the kind of practice students need to learn and retain basic multiplication
and division facts.
Blackline NC F 38
Blackline NC F 37
NAME
NAME
DATE
DATE
Fact Fluency with 8’s Practice Multiplying by 8 & 4
Fact Fluency with 8’s Multiplying & Dividing by 8
MULTIPLICATION FACT FLUENCY
MULTIPLICATION FACT FLUENCY
Strategy
How It Works
Example
Double-Double-Doubles
To multiply any number by 8,
double the number 3 times.
What is 8 × 7?
It’s 7 doubled 3 times,
Double once: 7 + 7 = 14
Double twice: 14 + 14 = 28
Double three times:
28 + 28 = 56
1
Circle all the double-double-doubles (×8) in blue. Then go back and fill in the
answers with regular pencil.
2
Circle all the double-doubles (×4) in red. Then go back and fill in the answers
with regular pencil.
9
3
6
8
11
7
9
×8
×8
×8
×8
×4
×4
×4
____
____
____
____
____
____
____
1
Multiply each number in the grid by 8. Write each product in the box. The first
one is done for you.
5
7
3
9
11
8
12
6
2
10
8
11
1
9
5
0
12
4
40
2
3
Use the double-double-doubles strategy to help solve these combinations.
8 × 15 = ______
14
×8
____
3
8 × 25 = ______
150
×8
____
8 × 35 = ______
40 ÷ 8 = ______
8 80
88 ÷ 8 = ______
8 48
72 ÷ 8 = ______
8 56
64 ÷ 8 = ______
8 96
12
×8
____
10
×8
____
9
×8
____
3
×4
____
5
×8
____
4
×4
____
7
×8
____
6
×4
____
11
×8
____
9
×4
____
4
×8
____
8
×8
____
Write two multiplication and two division facts for each set of numbers.
b
c
8
7
Use what you know about multiplying by 8 to solve these division problems.
5
×4
____
a
8 × 50 = ______
30
×8
____
2
×8
____
d
9
56
8
8
12
72
96
8
6
48
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
Bridges Breakouts • 5
Grade 4
Building Computational Fluency
Building Computational Fluency Blackline F 76
Building Computational Fluency Blackline F 78
NAME
DATE
NAME
Fact Fluency with 6’s–12’s Secret Path Problems, Set 1
Fact Fluency with 6’s–12’s Division Capture
MULTIPLICATION FACT FLUENCY
MULTIPLICATION FACT FLUENCY
• Find a path through all of the numbers in each set by multiplying or dividing
to get from one number to the next.
• You have to use each number just one time.
• You can move only 1 space at a time. You can move over, up, down, or
diagonally.
• Every path has a start point and an end point. Circle them both.
• You can also go backwards. Try to start at the end point and go back to the
start point.
example
9
6 × 5 takes
you to 30.
Try this one. The start and end points have
been
marked for
9
you.
9 × 4 takes
you to 36.
30
6
4
5
6
36
DATE
36 ÷ 6 takes
you to 6.
72
8
6
12
6
48
4
You’ll need
H a partner
H 2 pencils or markers in different colors
H paperclip and pencil to use as a spinner
Instructions for Division Capture 6’s–12’s
1
Take turns spinning the spinner.
The player who gets the higher number goes first.
Try to capture 3 or 4 boxes in a
row: across, up and down, or diagonally. Keep playing until the gameboard
is filled or neither player can use the
number he or she spins 3 times in a
row.
5 Then circle the places on the grid
where you got 3 or 4 in a row and add
up your scores.
6
2
12
Take turns spinning the spinner.
Use the number you spin to complete
one of the division problems below. Be
sure to use your own color pencil.
7
8
11
3
If the box you need is already filled,
you lose your turn.
9
Find your own start and end points, as well as a path through the numbers.
1
2
4
3
6
12
7
6
9
9
12 72
96
8
6
42
6
36
54
9
8
9
72
4
5
4
8
6
120
8
36
9
3
12
12
5
48
5
40
6
6
27
10
6
60
12
4
10
6 • Bridges Breakouts
42 ÷
=7
81 ÷
=9
96 ÷
= 12
121 ÷
= 11
63 ÷
=7
54 ÷
=9
49 ÷
=7
72 ÷
=8
54 ÷
=6
56 ÷
=8
72 ÷
=6
72 ÷
= 12
63 ÷
=9
108 ÷
=9
64 ÷
=8
132 ÷
= 12
144 ÷
= 12
84 ÷
= 12
88 ÷
=8
56 ÷
=7
Scoring
3 in a Row—1 point
4 in a Row—2 points
Player 1 Points
Player 2 Points
Grade 4
Building Computational Fluency
Assessment 1
ASSESSMENT
Overview
You’ll need
This assessment is designed to help gauge
students’ key math skills early in the school
year. You’ll find support suggestions on
page 9.
H Assessment 1, pages 1–5 (pages 11–15,
class set)
Timing
Early in the school year or at any other
time appropriate for your students
Skills & Concepts
H demonstrating fluency with basic
addition and subtraction facts
H Assessment 1 Class Checklist, pages 1
and 2 (pages 21 and 22, optional, run
2 or 3 copies as needed)
H base ten pieces for students who want
to use them (Use page 16 to run about
a one-third class set of base ten pieces
if needed.)
H demonstrating fluency with multiplication facts through 6 × 6
H money value pieces for students who
want to use them (Use pages 17–19
to run about a one-third class set of
money value pieces if needed.)
H adding and subtracting 2- and 3-digit
numbers and money amounts with
regrouping
H paper bills for those students who
want to use them (Use page 2 if
needed.)
H identifying place value of digits in
whole numbers
H real or plastic coins for students who
want to use them (if you have them)
H multiplying and dividing 2- and 3-digit
numbers by 1-digit numbers
H half-class set of student clocks
H counting and computing with money
H determining elapsed time
H telling time to the minute
Conducting Assessment 1
We recommend that you administer Assessment 1 within the first two weeks
of school to get a sense of students’ comfort level with key concepts and
skills. This assessment may also prove useful if you don’t already have your
own school or district instrument for gauging the skills of your incoming
fourth graders. Plan to conduct the 4-page test during a single math period or
break it out over 2 or more days, depending on your schedule and the needs
of your students.
The first page is a set of 20 addition facts and a set of 20 subtraction facts,
and the second is a set of 40 multiplication facts through 6 × 6. You’ll probBridges Breakouts • 7
Grade 4
Building Computational Fluency
Assessment 1 (cont.)
ably want to conduct these two pages of the assessment as a timed test, allowing 2 or 3 minutes for each page with a stretch break in between. While
we don’t ordinarily advocate timed testing, it is one way to get a quick read
on students’ current levels of comfort and fluency with basic facts. Reassure
students that if they can’t complete one or both sets of facts in the given time,
they’ll have plenty of opportunity to develop and demonstrate their skills
with these facts (and more) over the coming months.
For the rest of the assessment, make manipulatives available to those students who want to use them, and encourage students to be as complete as
possible in showing their solution methods; the answer alone will not give
you enough information about what students understand. While many of
your students may be using their own invented algorithms for adding and
subtracting multi-digit numbers, and may actually need to show their work
to find the answer, we strongly suggest that you also require students who
are using the standard algorithms for these computations to explain their
thinking and their notation. If, for instance, they have crossed out numbers
or placed extra numbers at the tops of columns, have them explain what their
cross-outs and extra numbers mean, directly on the assessment sheet, using
words, numbers, and sketches if possible.
The material on page 4 examines students’ current skills and strategies with
multiplication beyond the basics and division with and without remainders,
as well as their understanding of fractions. On the fourth page, students
count money, add money, make change, tell time, and calculate elapsed time.
Depending on your district expectations, and your students’ experiences in
third grade, you may want to reassure students that they’re not expected to
be able to complete all of these problems. Invite them to write “I don’t know
yet” under the items they are not able to solve or do not know how to begin.
Using Information from Assessment 1
You can use the Assessment 1 Class Checklist to compile assessment results
and get an overview of students’ strengths, as well as the areas in which
they’ll need more work.
We most often use the results of the Assessment 1 to guide our own instruction but you can also use at least the first three pages of the assessment to
gauge whether or not your incoming fourth graders are working at grade
level. Depending on your district expectations, you might take a closer look
at students who aren’t able to complete at least 24 (70%) of the basic addition
and subtraction facts within the 2 or 3-minute period allotted, or 24 (70%) of
the multiplication facts on page 2, which only include those facts students are
generally expected to master in third grade. (Students who are able to com8 • Bridges Breakouts
Grade 4
Building Computational Fluency
Assessment 1 (cont.)
plete 40 facts correctly in 2 minutes are working at a rate of 3 seconds per
fact, which is generally deemed to indicate fluency. This early in the school
year, however, you might be satisfied with the slightly slower rate of 4.5 seconds per fact allowed by a 3-minute timing.) Likewise, students who have
not yet developed efficient methods for adding and subtracting 2- and 3-digit
numbers or calculating with money and time will need extra support. We
tend to worry less about students who aren’t yet working efficiently with multiplication, division, and fractions, as these are topics that will receive considerable coverage in fourth grade.
SUPPORT ACTIVITIES
You may discover that some of your students need a considerable amount of
support in learning either their basic addition and subtraction facts, developing
efficient strategies for multi-digit addition or subtraction, working with money,
and/or telling time and computing elapsed time. You will find a number of
games and activities in the second section of this packet that you can use to provide more support for these students. (See Blackline S for addional information.)
SUPPORT ACTIVITIES
Activity
Name
Topic
Activity 1
Spinning Around Subtraction
Subtraction facts to 20
Activity 2
More or Less Place Value
Place value to hundreds place
Activity 3
Make 100
2-digit addition
Activity 4
Race to 100 & Back
Basic addition and 2-digit addition
Activity 5
Count Down 400
2- and 3-digit subtraction
Activity 6
More or Less Addition
2-digit addition
Activity 7
More or Less Subtraction
2-digit subtraction
Activity 8
Three Turns to Win
Adding money to $5
Activity 9
Finish with $10
Adding and subtracting money to $10
Activity 10
An Hour or Bust to the Minute
Elapsed time to the minute
Activity 11
Get Me to the Bus on Time
Elapsed time to the minute
Bridges Breakouts • 9
Grade 4
Building Computational Fluency
Assessment 1 Answer Key
ANSWER KEY
Pages 11–15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Row 1: 12, 15, 13, 16, 16, 14, 11
Row 2: 17, 10, 14, 12, 15, 14, 10
Row 3: 19, 12, 13, 18, 12, 11
Row 1: 7, 4, 5, 8, 7, 3, 6
Row 2: 5, 10, 4, 7, 6, 10, 8
Row 3: 8, 8, 9, 5, 6, 5
Row 1: 6, 4, 5, 4, 4, 1, 0
Row 2: 5, 0, 6, 8, 9, 30, 12
Row 3: 10, 24, 18, 8, 3, 10, 20
Row 4: 6, 2, 15, 12, 15, 18, 6
Row 5: 20, 36, 32, 12, 16, 24, 2
Row 6: 12, 0, 3, 30, 25
211
$4.92
117
$1.28
123, 254, 1023, 2045
84
1000
4
3, remainder 1
second choice
third choice
$11.90
$3.40
clock a
a 7:25
b 7:15
c 10:23
d 8:05
10 • Bridges Breakouts
Building Computational Fluency Blackline
NAME
DATE
Assessment 1 page 1 of 5
1
2
Solve these addition problems.
6
+6
____
6
+9
____
6
+7
____
8
+8
____
9
+7
____
9
+5
____
8
+3
____
8
+9
____
7
+3
____
8
+6
____
8
+4
____
7
+8
____
7
+7
____
4
+6
____
9
+
10
____
5
+7
____
8
+5
____
9
+9
____
9
+3
____
4
+7
____
Solve these subtraction problems.
14
–7
____
14
– 10
____
15
– 10
____
16
–8
____
15
–8
____
11
–8
____
14
–8
____
14
–9
____
13
–3
____
12
–8
____
16
–9
____
13
–7
____
19
–9
____
18
– 10
____
13
–5
____
17
–9
____
15
–6
____
13
–8
____
15
–9
____
12
–7
____
© The Math Learning Center
Bridges Breakouts
11
Building Computational Fluency Blackline
NAME
DATE
Assessment 1 page 2 of 5
3
12
Solve these multiplication problems.
6
×1
____
1
×4
____
5
×1
____
2
×2
____
4
×1
____
1
×1
____
5
×0
____
1
×5
____
2
×0
____
3
×2
____
2
×4
____
3
×3
____
5
×6
____
6
×2
____
5
×2
____
4
×6
____
3
×6
____
4
×2
____
3
×1
____
2
×5
____
4
×5
____
1
×6
____
1
×2
____
5
×3
____
4
×3
____
3
×5
____
6
×3
____
2
×3
____
5
×4
____
6
×6
____
8
×4
____
3
×4
____
4
×4
____
6
×4
____
2
×1
____
2
×6
____
3
×0
____
1
×3
____
6
×5
____
5
×5
____
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline
NAME
DATE
Assessment 1 page 3 of 5
Show all your work and explain your thinking for problems 4, 5, 6, and 7.
4
123
+ 88
_____
5
$3.69 + $1.23 =
6
304
– 187
_____
7
$5.00 – $3.72 =
8
In the spaces below, write the following numbers in order from least to
greatest.
2,045
least
© The Math Learning Center
123
254
1,023
greatest
Bridges Breakouts
13
Building Computational Fluency Blackline
NAME
DATE
Assessment 1 page 4 of 5
Show all your work and explain your thinking for problems 9, 10, 11, and 12.
14
9
14
×6
_____
10
11
24 ÷ 6 =
12
200
×5
_____
13 ÷ 4 =
13
Which rectangle is
14
Which rectangle shows a fraction that is equal to
Bridges Breakouts
1
3
gray?
1
3
?
© The Math Learning Center
Building Computational Fluency Blackline
NAME
DATE
Assessment 1 page 5 of 5
15
How much money does David have to spend at the garage sale? Count
all of the money here and record the amount in the box.
David’s Money
16
If David bought 2 video games, 1 stuffed animal, and 3 action figures,
how much money did he have left?
Item
Video Game
Board Game
Action Figure
Stuffed Animal
Cost per Item
$3.50
$1.25
25¢
75¢
17
It is 7:10 and Anna has to catch the bus in 15 minutes. Which clock
shows the time Anna has to catch the bus?
a
b
c
18 What time does each clock above show?
a __________________________
c
b __________________________
d
© The Math Learning Center
d
__________________________
__________________________
Bridges Breakouts
15
Building Computational Fluency Blackline Run 1 copy on cardstock per student as needed and cut out along heavy lines.
Base Ten Pieces
16
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline Run 1 copy on cardstock for each student as needed and cut out pieces along heavy lines.
Money Value Pieces page 1 of 3
© The Math Learning Center
Bridges Breakouts
17
Building Computational Fluency Blackline Run 1 copy on cardstock for each student as needed and cut out pieces along heavy lines.
Money Value Pieces page 2 of 3
18
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline Run 1 copy on cardstock for each student as needed and cut out pieces along heavy lines.
Money Value Pieces page 3 of 3
© The Math Learning Center
Bridges Breakouts
19
Building Computational Fluency Blackline Run copies on green paper and cut out along heavy lines as needed.
Paper Bills
20
Bridges Breakouts
© The Math Learning Center
Bridges Breakouts
11b shows work
11a divides 24 ÷ 6
10b shows work
10a multiplies 200 × 5
9b shows work
9a multiplies 14 × 6
8 orders multi-digit numbers
7b shows work
7a subtracts money amounts with regrouping
6b shows work
6a subtracts with regrouping
5b shows work
5a adds money amounts with regrouping
4b shows work
ent
Na
Stud
© The Math Learning Center
1 & 2 completes 24 out of 40 addition and
subtraction facts in 2 minutes
3 completes 24 out of 40 multiplication
facts in 2 minutes
4a adds with regrouping
mes
Assessment 1 Class Checklist page 1 of 2
Building Computational Fluency Blackline Run enough copies to record the results for all students in your class.
21
18 tells time to the minute
17 calculates elapsed time
16 does a multi-step money story problem
15 counts money accurately
14 identifies fraction equivalent to 1⁄3
13 identifies area model for 1⁄3
12b shows work
Stud
Bridges Breakouts
12a divides 13 ÷ 4
ent
Na
22
mes
Assessment 1 Class Checklist page 2 of 2
Building Computational Fluency Blackline Run enough copies to record the results for all students in your class.
© The Math Learning Center
Building Computational Fluency Blackline S
Support Activities
There are 29 activities in this collection. Most are games designed to be
played by partners or small groups, although some can be adapted for use
with an entire class at once. The Support Activities are listed by skill in the
table below, and are intended to supplement any intermediate math program.
Most involve the use of visual models and strategies, and are meant to help
students develop conceptual understandings as they gain increased fluency.
As you look through the collection, you may find some games you want to
use to help teach key computational skills to your whole class. Some teachers also run the game components on cardstock and laminate them to make
a durable set of “learning stations” available for use by students during free
time or to check out for home use.
STRATEGIES FOR BASIC SUBTRACTION FACTS
Activity
Name
Support Blackline Numbers
Support Activity 1
Spinning Around Subtraction
S 1.1–1.8
BASIC MULTIPLICATION FACTS
Activity
Name
Support Blackline Numbers
Support Activity 12
Spinning Around Multiplication
S 12.1–12.6
Support Activity 13
Array Challenge
S 13.1–13.5
Support Activity 14
Multiplication Challenge
S 14.1–14.5
Support Activity 15
Spinning for Arrays
S 15.1–15.7
Support Activity 16
Product Bingo
S 16.1–16.4
BASIC MULTIPLICATION & DIVISION FACTS
Activity
Name
Support Blackline Numbers
Support Activity 17
What’s Missing? Bingo
S 17.1–17.8
Support Activity 23
Remainders Win
S 23.1–23.6
PLACE VALUE
Activity
Name
Support Blackline Numbers
Support Activity 2
More or Less Place Value
S 2.1–2.8
ADDING & SUBTRACTING MULTI-DIGIT NUMBERS
Activity
Name
Support Blackline Numbers
Support Activity 3
Make 100
S 3.1–3.8
Support Activity 4
Race to 100 & Back
S 4.1–4.6
Support Activity 5
Count Down 400
S 5.1–5.4
Support Activity 6
More or Less Addition (2-digit)
S 6.1–6.8
Support Activity 7
More or Less Subtraction (2-digit)
S 7.1–7.6
Support Activity 18
More or Less Addition Big Time (3-digit)
S 18.1–18.6
Support Activity 19
More or Less Subtraction Big Time
(3-digit)
S 19.1–19.4
Support Activity 20
Larger Numbers on a Line (3-digit)
S 20.1–20.4
Support Activity 26
Round & Add Tens
S 26.1–26.5
Support Activity 27
Round & Add Hundreds
S 27.1–27.5
© The Math Learning Center
Bridges Breakouts  
Building Computational Fluency Blackline S
MULTIPLYING 1-DIGIT BY 2-DIGIT NUMBERS
Activity
Name
Support Blackline Numbers
Support Activity 22
Spin & Multiply
S 22.1–22.4
DIVIDING 2- & 3-DIGIT NUMBERS BY 1-DIGIT NUMBERS
Activity
Name
Support Blackline Numbers
Support Activity 28
Divide ‘Em Up
S 28.1–28.4
ADDING & SUBTRACTING WITH MONEY
Activity
Name
Support Blackline Numbers
Support Activity 8
Three Turns to Win
S 8.1–8.6
Support Activity 9
Finish with $10
S 9.1–9.8
Activity
Name
Support Blackline Numbers
Support Activity 10
An Hour or Bust to the Minute
S 10.1–10.4
Support Activity 11
Get Me to the Bus on Time
S 11.1–11.6
ELAPSED TIME
PERIMETER OF RECTANGLES
Activity
Name
Support Blackline Numbers
Support Activity 21
Perimeter Showdown
S 21.1–21.5
FRACTIONS
Activity
Name
Support Blackline Numbers
Support Activity 24
Fraction Race
S 24.1–24.7
Support Activity 25
Fraction Bingo
S 25.1–25.6
Money, Fraction & Decimal
S 29.1–29.7
Support Activity 29
Showdown
If you plan to use the activities for remediation rather than instructional
purposes, you’ll find that they’re most effective when used with targeted students by an educational assistant, parent volunteer, or title/resource teacher.
Based on students’ performance on the Building Computational Fluency assessments, you’ll be able to determine which individuals would benefit from
a particular Support Activity and can assign them to work with an adult on
that activity. You can also send specific activities home with students for extra practice with their families. In order to prepare the Support Activities for
use by other adults, we recommend creating a packet that contains the instructional considerations, game instructions, and materials. That way, you
can provide an instructional assistant or volunteer with the packet and ask
him or her to conduct specific activities with individuals or small groups in
need of help in one or more areas.
While you can run game cards on cardstock, you’ll find that paper copies of
the game components work nearly as well with intermediate students, who
can cut out their own playing cards and use a paper-clip and pencil arrangement for a spinner arrow. Because these games have been designed for use at

Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S
home as well as school, very few of them involve concrete manipulatives. Those
that do include blacklines for making the manipulatives (i.e., base 10 pieces or
money value pieces), and you may want to run these sheets on cardstock.
© The Math Learning Center
Bridges Breakouts  
Building Computational Fluency Blackline S

Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S 9.1
Support Activity 9 H Instructional Considerations
SUPPORT ACTIVITY 9
Finish with $10
Overview
You’ll need
In this game, players spend a day at home and in their
neighborhood. They start out with $5.00 and throughout
the day, they travel around a game board doing chores,
going shopping, and visiting friends and relatives. As they
go, they earn money, find money, lose money, and buy
things. The goal is to make it around the game board with
at least $10.
H Instructions for Finish with $10 (Blackline S 9.2)
Skills & Concepts
H 1 game marker for each player
H counting, adding, subtracting, and estimating money
amounts up to $5
H identifying and applying the operation needed to
solve a problem
H Finish with $10 Game Board (Blacklines S 9.3 and 9.4,
1 copy of each sheet taped together to form a game
board for each pair of players)
H plastic coins and paper bills or money value pieces
(Use Blacklines S 9.5–9.7 to make your own money
value pieces if needed.)
H pencil and paperclip to use as a spinner (1 set for
each pair of players)
H scratch paper for writing number sentences
and computing
H using models, pictures, and/or numbers to demonstrate the meaning of addition and subtraction
H translating problem-solving situations into expressions
and equations
In this game, players begin with $5.00 each. The goal is to make it around the game board and finish with
at least $10.00. Encourage students to keep track of their money using real or plastic and paper coins and
bills. Some students might also prefer to use the money value pieces to keep track of their money.
This game is not meant to be a test of students’ reading skills. Encourage them to read the words on their
own, but don’t hesitate to read out loud for them if needed. Each time you or the student lands on a new
space, invite the student to explain what’s happening. Will she add money to her collection or subtract
money from her collection? How could the problem be written as an equation? We want students to develop the ability to translate situations into appropriate and meaningful mathematical problems.
Students will also practice reading money amounts expressed as decimal numbers ($0.85), as well as whole
numbers of cents (85¢). They’ll also need to determine the total value of mixed collections of coins.
Occasionally, you might ask students to estimate how much more money they need to get to $10.00. Are
they close to $10.00? About how close? How can they tell? Encourage them to estimate rather than labor
over exact computations.
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 9.2
Support Activity 9
SUPPORT ACTIVITY
Finish with $10
You’ll need
H Instructions for Finish with $10 (Blackline S 9.2)
H Finish with $10 Game Board (Blacklines S 9.3 and 9.4, 1 copy of each sheet taped together to
form a game board for each pair of players)
H plastic coins and paper bills or money value pieces (Use Blacklines S 9.5–9.7 to make your
own money value pieces if needed.)
H 1 game marker for each player
H pencil and paperclip to use as a spinner (1 set for each pair of players)
H scratch paper for writing number sentences and computing
Instructions for Finish with $10
1
Begin by placing your game markers
on the start space. Each player begins
with $5.00.
Blackline NC S 9.3 Run 1 copy for each pair of players. Tape to Blackline NC S 9.4 to make the game board.
Blackline NC S 9.4 Run 1 copy for each pair of players. Cut on dotted line and tape to Blackline NC S 9.3.
Finish with $10 Game Board page 1 of 2
START
Begin with $5.00.
You find a quarter on the
ground and pick it up.
Finish with $10 Game Board page 2 of 2
Your sister pays
back the 85¢
she borrowed
from you.
Do you have
$10.00 or more?
If so, you win!
If not, keep going
until you do.
Move Ahead
3
You find 3 quarters and
4 dimes in the pocket of
your pants.
2
You unload the laundry
and find 2
and 2
.
your friend
buys one of
your baseball cards
you don’t
want for
75¢.
,4
You buy a bunch of
grapes for 50¢.
You drop 50¢
on the ground.
,
1
4
2
You earn $2
for washing
the dishes.
You buy a pack of
baseball cards
for $1.50.
Your grandma
gives you $3.65
as a gift
You buy a candy
bar for $0.55.
3
You find 3
quarters and
a nickel on the
sidewalk.
Spaces
Your mom gives you
$2.75 for your allowance.
Your neighbor
pays you
$2.00 for
feeding
his dog.
You find 3
and 2
quarters
in the sofa.
You buy a
bottle of juice
for 85¢.
3
Take turns spinning the spinner
and moving ahead. Whenever a player
lands on a space, he reads the words
and decides whether he should add
money to his collection or take money
away from his collection. He decides
what the problem is and shows it with
an equation.
4
Players keep track of their money
using coins and bills, numbers, or
money value pieces if they have them.
5
2
Take turns spinning the spinner using a pencil and paperclip. The player
with the higher spin goes first.
Bridges Breakouts
The first player to get to the last
space with at least $10.00 wins.
© The Math Learning Center
Building Computational Fluency Blackline S 9.3 Run 1 copy for each pair of players. Tape to Blackline S 9.4 to make the game board.
Finish with $10 Game Board page 1 of 2
START
Begin with $5.00.
You find a quarter on the
ground and pick it up.
Your sister pays
back the 85¢
she borrowed
from you.
Your mom gives you
$2.75 for your allowance.
You earn $2
for washing
the dishes.
Do you have
$10.00 or more?
If so, you win!
If not, keep going
until you do.
You find 3 quarters and
4 dimes in the pocket of
your pants.
You unload the laundry
and find 2
,4
,
and 2
.
Your friend
buys one of
your baseball cards
you don’t
want for
75¢.
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 9.4 Run 1 copy for each pair of players. Cut on dotted line and tape to Blackline S 9.3.
Finish with $10 Game Board page 2 of 2
You buy a bunch of
grapes for 50¢.
You drop 50¢
on the ground.
Move Ahead
3
2
1
4
2
Bridges Breakouts
Your grandma
gives you $3.65
as a gift
You buy a candy
bar for $0.55.
3
You find 3
quarters and
a nickel on the
sidewalk.
Spaces
You buy a pack of
baseball cards
for $1.50.
Your neighbor
pays you
$2.00 for
feeding
his dog.
You find 3
and 2
in the sofa.
You buy a
bottle of juice
for 85¢.
© The Math Learning Center
Building Computational Fluency Blackline S 9.5 Run 1 copy on cardstock for each player. Cut out along solid lines.
Money Value Pieces page 1 of 3
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 9.6 Run 1 copy on cardstock for each player. Cut out along solid lines.
Money Value Pieces page 2 of 3
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S 9.7 Run 1 copy on cardstock for each player. Cut out along solid lines.
Money Value Pieces page 3 of 3
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 9.8
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S 15.1
Support Activity 15 H Instructional Considerations
SUPPORT ACTIVITY
Spinning for Arrays
Overview
You’ll need
Players take turns spinning two number spinners and finding the product of the two numbers. Then, they select an
array card with an area that matches that product. They
can also add two array cards together if the sum of their
products is equal to the product of the two numbers
they spun. At the end of the game, the player with the
most cards wins.
H Instructions for Spinning for Arrays ( Blackline S 15.2)
H Spinning for Arrays Spinner ( Blackline S 15.3, 1 copy
for every 2 pairs of players, cut in half)
H Array Cards, pages 1–4 (Blacklines S 15.4–15.7, 1 copy
for each pair of players, cut apart and stored in an
envelope or resealable plastic bag)
H pencil and paperclip to use as a spinner
Skills & Concepts
H practicing multiplication facts through 8 × 10
H finding factors of whole numbers to 100 using an
understanding of number relationships and models
such as arrays
H applying the commutative, associative, and distributive properties to calculations with whole numbers
H relating the area of a rectangle and its dimensions to
area models for multiplication and division
Encourage students to think carefully about how they organize the cards at the beginning of the game.
After playing a few rounds, they may have a better sense of how to organize the cards in the most helpful way. Some may want to organize them by common factor, but players will likely find it most helpful
to organize the cards by product.
When they begin playing this game, many students will search for arrays that have dimensions equal to
the two numbers they spun. As they get used to the game, encourage them to search for arrays with different dimensions whose areas are equal to the target product. As they become more fluent with their
facts, challenge them to add the areas of two or more arrays to reach their target product. You might
first have them practice finding pairs of products whose sum is equal to a target product.
Blackline NC S 15.3 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Spinning for Arrays Spinners
8
7
© The Math Learning Center
3
6
4
5
×
6
5
7
10
8
9
4×6
Blackline NC S 15.4 Array Card
4 × 6 = 24
3×8
Blackline NC S 15.4 Array Card
3 × 8 = 24
Bridges Breakouts
Building Computational Fluency Blackline S 15.2
Support Activity 15
SUPPORT ACTIVITY
Spinning for Arrays
You’ll need
H Instructions for Spinning for Arrays ( Blackline S 15.2)
H Spinning for Arrays Spinner ( Blackline S 15.3, 1 copy for every 2 pairs of players, cut in half)
H Array Cards, pages 1–4 (Blacklines S 15.4–15.7, 1 copy for each pair of players, cut apart
and stored in an envelope or resealable plastic bag)
H pencil and paperclip to use as a spinner
Instructions for Spinning for Arrays
1
Work with your partner to set out the
Array Cards so that it will be easy for
you to find a specific card when you
need it. Then decide who will go first
using any method you like.
6×8
B l a c k l i n e N C S 1 5. 6 A r r a y C a r d
2
Spin both spinners and multiply the
two numbers.
3
Then find a card that shows an array whose total area is the same as the
product you just computed. You could
also add together the products of more
than one card to make the total and
then take those cards.
Blackline NC S 15.3 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Spinning for Arrays Spinners
8
7
3
6
Bridges Breakouts
4
5
×
6 × 8 = 48
4×6
or
3×8
Blackline NC S 15.4 Array Card
Blackline NC S 15.4 Array Card
4 × 6 = 24
3 × 8 = 24
6 times 8 is 48. I could take the 6 times 8 card.
Or I could add these two cards together.
8 times 3 is 24 and so is 4 times 6. So add 24
and 24 and that’s 48.
4
If you can’t find any card or combination of cards to match the product,
you lose that turn.
5
6
5
7
10
8
9
Continue to take turns until all the
cards have been taken. Then count up
your cards. The player with the most
cards at the end wins.
© The Math Learning Center
Building Computational Fluency Blackline S 15.3 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Spinning for Arrays Spinner
8
7
3
6
4
5
×
6
5
7
10
8
9
Spinning for Arrays Spinner
8
7
© The Math Learning Center
3
6
4
5
×
6
5
7
10
8
9
Bridges Breakouts
Bridges Breakouts
Blackline NC S 15.4 Array Card
Blackline NC S 15.4 Array Card
3 × 10
Blackline NC S 15.4 Array Card
Blackline NC S 15.4 Array Card
3×9
6×3
3×5
Blackline NC S 15.4 Array Card
5×4
Blackline NC S 15.4 Array Card
7×3
Blackline NC S 15.4 Array Card
4×6
Blackline NC S 15.4 Array Card
3×8
Building Computational Fluency Blackline S 15.4 Run 1 copy for each pair of players. Cut apart and store in an envelope or resealable plastic bag.
Array Cards page 1 of 4
© The Math Learning Center
© The Math Learning Center
5×6
Blackline NC S 15.5 Array Card
Blackline NC S 15.5 Array Card
Blackline NC S 15.5 Array Card
Blackline NC S 15.5 Array Card
5×5
8×4
4×7
Bridges Breakouts
Blackline NC S 15.5 Array Card
5×7
Blackline NC S 15.5 Array Card
4×9
Blackline NC S 15.5 Array Card
8×5
Blackline NC S 15.5 Array Card
10 × 4
Building Computational Fluency Blackline S 15.5 Run 1 copy for each pair of players. Cut apart and store in an envelope or resealable plastic bag.
Array Cards page 2 of 4
Bridges Breakouts
6×8
Blackline NC S 15.6 Array Card
Blackline NC S 15.6 Array Card
Blackline NC S 15.6 Array Card
5 × 10
7×6
Blackline NC S 15.6 Array Card
9×5
Blackline NC S 15.6 Array Card
9×6
Blackline NC S 15.6 Array Card
6×5
Blackline NC S 15.6 Array Card
10 × 6
Blackline NC S 15.6 Array Card
6×6
Building Computational Fluency Blackline S 15.6 Run 1 copy for each pair of players. Cut apart and store in an envelope or resealable plastic bag.
Array Cards page 3 of 4
© The Math Learning Center
© The Math Learning Center
8×9
Blackline NC S 15.7 Array Card
Blackline NC S 15.7 Array Card
Blackline NC S 15.7 Array Card
Blackline NC S 15.7 Array Card
8×8
7×8
7×7
Bridges Breakouts
Blackline NC S 15.7 Array Card
10 × 8
Blackline NC S 15.7 Array Card
9×7
Blackline NC S 15.7 Array Card
3×5
Blackline NC S 15.7 Array Card
7 × 10
Building Computational Fluency Blackline S 15.7 Run 1 copy for each pair of players. Cut apart and store in an envelope or resealable plastic bag.
Array Cards page 4 of 4
Building Computational Fluency Blackline S 15.8
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S 17.1
Support Activity 17 H Instructional Considerations
SUPPORT ACTIVITY
What’s Missing? Bingo
Overview
You’ll need
Students take turns drawing cards, each of which features
an equation that is missing a single number. Students
determine what the missing number is and draw an X
over that number on their bingo boards. The first player to
get 4 numbers in a row wins.
H Instructions for What’s Missing? Bingo ( Blackline S
17.2)
Skills & Concepts
H using models, pictures, and numbers to demonstrate an understanding of multiplication/division
as repeated addition/subtraction, equal groups of
objects, arrays, or skip counting
H What’s Missing? Bingo Boards ( Blackline S 17.3, 1 copy
per player)
H What’s Missing? Bingo Cards, pages 1–4 (Blacklines S
17.4–17.7, 1 copy for each pair of players, cut apart and
stored in an envelope or resealable plastic bag)
H Grid Paper ( Blackline S 17.8, 1 copy for each player)
H demonstrating computational fluency with multiplication facts up to 5 × 10
H developing and using strategies for multiplication facts
up to 10 × 10
H solving for an unknown number in an equation
This bingo game helps students develop an explicit understanding of the inverse relationship between
multiplication and division, which is key to their ability to solve missing factor problems and to their fluency with division facts. It also provides an opportunity for students to practice applying the commutative property of multiplication. If you find students are still struggling with multiplication facts, have
them go back and use one of the multiplication support games to shore up their skills with multiplication before playing this game, which involves quite a bit of division practice.
You may need to remind players to select just one board on the sheet for each game and to make sure that
they are using different boards from each other. Students can use a single sheet to play 4 separate games.
Blackline NC S 17.3 Run 1 copy for each player.
NAME
Sage
DATE
Feb. 10
What’s Missing? Bingo Boards
Board 1
Board 2
2
6
7
3
10
3
5
4
5
4
9
2
6
4
9
7
4
7
5
8
9
5
6
3
3
8
6
10
8
3
7
2
7×
= 35
Bla ckli ne NC
S 17. 5 Wh at’s
Mis sing ? Bing
o Car d
Board 3
© The Math Learning Center
Board 4
7
4
8
6
3
5
6
10
3
9
10
3
7
2
9
8
Bridges Breakouts
Building Computational Fluency Blackline S 17.2
Support Activity 17
SUPPORT ACTIVITY
What’s Missing? Bingo
You’ll need
H Instructions for What’s Missing? Bingo ( Blackline S 17.2)
H What’s Missing? Bingo Boards ( Blackline S 17.3, 1 copy per player)
H What’s Missing? Bingo Cards, pages 1–4 (Blacklines S 17.4–17.7, 1 copy for each pair of
players, cut apart and stored in an envelope or resealable plastic bag)
H Grid Paper ( Blackline S 17.8, 1 copy for each player)
Instructions for What’s Missing? Bingo
1
Pick a bingo board that is different
from your partner’s. Select just one
bingo board each per game.
Blackline NC S 17.3 Run 1 copy for each player.
Board 1
Decide who will go first and put the
cards between you in a stack, face down.
3
Draw a card and determine what
the missing number is. Talk to your
partner and make sure you agree. You
can draw on the grid paper if you like.
2
6
7
3
10
3
5
4
5
4
9
2
6
4
9
7
4
7
5
8
9
5
6
3
3
8
6
10
8
3
7
2
Board 3
Board 4
7
Nicole
4
8
6
3
3
9Board10
1
3
7
2Board 29
8
2
5
6
2
7
7
3
9
10
5
3
4
5
6
4
3
5
8
4
5
9
6
2
4
6
8
4
9
9
7
7
4
4
7
5
8
9
5
6
3
3
8
6
10
8
3
7
2
NAME
What’s Missing? Bingo Boards
Blackline NC S 17.5 What’s Missing? Bingo Card
Bridges Breakouts
Feb. 10
Board 2
Blackline NC S 17.3 Run 1 copy for each player.
Hmm. This means that
something times 7 is 35.
7×
= 35
What times 7 is 35? …
Oh! I remember. The 7 in
the clock is 35 minutes, so it has to be 5, because the numbers on the clock count by 5’s.
Draw an X over the missing number if it appears on your bingo board.
Some numbers may appear more than
once, so think carefully about where
you draw the X.
DATE
What’s Missing? Bingo Boards
2
4
Sage
NAME
DATE
5
Number Corner
Feb. 10
6
10
© The Math Learning Center
I have twoBoard5’s3 on here, but if IBoard
put4 my X here,
I can 7win!4 8 6
3
5
6
10
5
7
2
9
8
10
3
3
9
Take
turns
drawing
cards
until
one
5 a row
4
6to win.
3
5 gets
2 47 numbers
9
player
in
8
5
6
4
8
9
7
4
© The Math Learning Center
Building Computational Fluency Blackline S 17.3 Run 1 copy for each player.
NAME
DATE
What’s Missing? Bingo Boards
Board 1
Board 2
2
6
7
3
10
3
5
4
5
4
9
2
6
4
9
7
4
7
5
8
9
5
6
3
3
8
6
10
8
3
7
2
Board 3
Board 4
7
4
8
6
3
5
6
10
3
9
10
3
7
2
9
8
5
2
7
9
5
4
6
3
8
5
6
4
8
9
7
4
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 17.4 Run 1 copy for each pair of players. Cut cards apart and store in an envelope or resealable plastic
What’s Missing? Bingo Cards page 1 of 4
9×
= 18
Blackline NC S 17.4 What’s Missing? Bingo Card
5×
= 30
Blackline NC S 17.4 What’s Missing? Bingo Card
7×
= 14
Blackline NC S 17.4 What’s Missing? Bingo Card
3×
= 18
Blackline NC S 17.4 What’s Missing? Bingo Card
Bridges Breakouts
× 7 = 21
Blackline NC S 17.4 What’s Missing? Bingo Card
× 7 = 49
Blackline NC S 17.4 What’s Missing? Bingo Card
× 8 = 24
Blackline NC S 17.4 What’s Missing? Bingo Card
× 8 = 56
Blackline NC S 17.4 What’s Missing? Bingo Card
© The Math Learning Center
Building Computational Fluency Blackline S 17.5 Run 1 copy for each pair of players. Cut cards apart and store in an envelope or resealable plastic
What’s Missing? Bingo Cards page 2 of 4
× 8 = 32
Blackline NC S 17.5 What’s Missing? Bingo Card
× 3 = 24
Blackline NC S 17.5 What’s Missing? Bingo Card
× 6 = 24
Blackline NC S 17.5 What’s Missing? Bingo Card
× 4 = 32
Blackline NC S 17.5 What’s Missing? Bingo Card
© The Math Learning Center
× 5 = 25
Blackline NC S 17.5 What’s Missing? Bingo Card
6×
= 54
Blackline NC S 17.5 What’s Missing? Bingo Card
7×
= 35
Blackline NC S 17.5 What’s Missing? Bingo Card
8×
= 80
Blackline NC S 17.5 What’s Missing? Bingo Card
Bridges Breakouts
Building Computational Fluency Blackline S 17.6 Run 1 copy for each pair of players. Cut cards apart and store in an envelope or resealable plastic
What’s Missing? Bingo Cards page 3 of 4
16 ÷
=8
Blackline NC S 17.6 What’s Missing? Bingo Card
÷3=2
Blackline NC S 17.6 What’s Missing? Bingo Card
÷5=2
Blackline NC S 17.6 What’s Missing? Bingo Card
÷2=3
Blackline NC S 17.6 What’s Missing? Bingo Card
Bridges Breakouts
21 ÷
=7
Blackline NC S 17.6 What’s Missing? Bingo Card
14 ÷
=2
Blackline NC S 17.6 What’s Missing? Bingo Card
18 ÷
=6
Blackline NC S 17.6 What’s Missing? Bingo Card
49 ÷
=7
Blackline NC S 17.6 What’s Missing? Bingo Card
© The Math Learning Center
Building Computational Fluency Blackline S 17.7 Run 1 copy for each pair of players. Cut cards apart and store in an envelope or resealable plastic
What’s Missing? Bingo Cards page 4 of 4
12 ÷
=3
Blackline NC S 17.7 What’s Missing? Bingo Card
32 ÷
=4
Blackline NC S 17.7 What’s Missing? Bingo Card
8÷
=2
Blackline NC S 17.7 What’s Missing? Bingo Card
÷4=2
Blackline NC S 17.7 What’s Missing? Bingo Card
© The Math Learning Center
40 ÷
=8
Blackline NC S 17.7 What’s Missing? Bingo Card
÷3=3
Blackline NC S 17.7 What’s Missing? Bingo Card
35 ÷
=7
Blackline NC S 17.7 What’s Missing? Bingo Card
27 ÷
=3
Blackline NC S 17.7 What’s Missing? Bingo Card
Bridges Breakouts
Building Computational Fluency Blackline S 17.8 Run 1 copy for each player.
Grid Paper
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline S 22.1
Support Activity 22 H Instructional Considerations
SUPPORT ACTIVITY
Spin & Multiply
Overview
You’ll need
Players take turns spinning 1-by-2-digit multiplication combinations. After they have each taken 3 turns, they find the sum
of their 3 products. The player with the larger sum wins.
H Instructions for Spin & Multiply (Blackline S 22.2)
Skills & Concepts
H multiplying 1-digit numbers by 2-digit numbers
H Spin & Multiply Record Sheet (Blackline S 22.4, 1 copy
per player)
H adding 2- and 3-digit numbers
H paperclip and pencil for use as a spinner
H Spin & Multiply Spinner (Blackline S 22.3, 1 copy for
every 2 pairs of players, cut in half)
It may be helpful if, before students play a full game of Spin & Multiply, you model how to sketch the
frame and then the array for a 1-by-2-digit combination. As they compute their products, encourage
players to think in chunks and use friendly numbers.
24
DATE
Player 2
7
April 8
Mr. Britt
Blackline NC S 22.4 Run 1 copy for each player.
Alec
S p i n & M u l t i p l y R e co r d S h e e t
Player 1
Alec
NA ME
Alec I can do 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 130, 140. And then add 7 times 4.
Mr. Britt Alec, is there any way you could have gotten the 140 part without counting each ten?
Total
Total
Alec Umm, well, I could count down by 20’s. Oh! Or I could see it’s 70 plus 70. That’s a fast way to
get 140.
Students who are working more fluently might be encouraged, if they don’t come up with it on their
own, to think about 7 × 25 to solve 7 × 24. Working with landmark numbers and then adjusting their
answers can be a quick way to work mentally. (e.g., 7 × 25 = 175 and 175 – 7 = 168. So 7 × 24 is 168.)
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 22.2
Support Activity 22
SUPPORT ACTIVITY
Spin & Multiply
You’ll need
H Instructions for Spin & Multiply (Blackline S 22.2)
H Spin & Multiply Spinner (Blackline S 22.3, 1 copy for every 2 pairs of players, cut in half)
H Spin & Multiply Record Sheet (Blackline S 22.4, 1 copy per player)
H paperclip and pencil for use as a spinner
Instructions for Spin & Multiply
Record both players’ names on a
Spin & Multiply Record Sheet.
2
Spin each spinner to get two numbers to multiply.
NA ME
Conner
S p i n & M u l t i p l y R e co r d S h e e t
Player 1
Conner
24
DATE
Player 2
April 8
Alena
140
+ 28
168
7 x 24 = 168
7
70 + 70 = 140
14 + 14 = 28
Blackline NC S 22.4 Run 1 copy for each player.
1
Blackline NC S 22.3 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Spin & Multiply Spinner
8
7
3
3
6
4
5
×
24
17
13
26
14
23
Spin & Multiply Spinner
Sketch the frame of linear pieces
onto the grid
13 first,
3 on the record sheet
8 fill in4 the array.24
and then
Explain14how
you computed
17of those
23
7
5the product
two factors6to your partner. 26
×
Number Corner
Bridges Breakouts
I drew the array to show the tens and ones.
First I saw the 70 plus 70. I forgot 7 times 4 is
28, but I saw it was 14 plus 14. 140 plus 28 is
168. That means 7 times 24 is 168.
Total
Total
4
You and your partner will each take
3 turns spinning, sketching, and finding the product.
5
When you have both taken 3 turns,
find the sums of your products. Double-check each other’s work.
6
The player with the larger sum
wins the game.
© The Math Learning Center
© The Math Learning Center
Building Computational Fluency Blackline S 22.3 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Spin & Multiply Spinner
8
7
3
6
4
5
×
24
17
13
26
14
23
Spin & Multiply Spinner
8
7
© The Math Learning Center
3
6
4
5
×
24
17
13
26
14
23
Bridges Breakouts
Bridges Breakouts
Total
Total
Player 1
Spin & Multiply Record Sheet
NAME
Player 2
DATE
Building Computational Fluency Blackline S 22.4 Run 1 copy for each player.
© The Math Learning Center
Building Computational Fluency Blackline S 23.1
Support Activity 23 H Instructional Considerations
SUPPORT ACTIVITY
Remainders Win
Overview
You’ll need
Players take turns completing multiplication and division calculations that often result in remainders. Players keep track of
their remainders and then add them up after they have each
taken 10 turns. The player with the highest sum wins.
H Instructions for Remainders Win (Blacklines NC S 23.2
and 23.3, 1 copy of each run back-to-back)
Skills & Concepts
H Remainders Win Record Sheet (Blackline S 23.5,
H Divisor Spinner (Blackline S 23.4, 1 copy for every 2
pairs of players, cut in half)
1 copy for each player)
H practicing multiplication facts through 9 × 9
H completing division facts with divisors to 10, including
those resulting in remainders
H Array Challenge Cards, pages 1–3 (Blacklines NC S
13.3–13.5, 1 copy cut apart for each pair of players)
H Number Charts (Blackline S 23.6, 1 copy for each
player, optional)
H paper clip and pencil to use as a spinner
If students have difficulty solving the division problems, encourage them to make use of the multiplication facts they already know, as well as count-by’s or repeated subtraction. In a few cases, they may
want to copy one of the arrays onto a Number Chart and then circle equal groups to divide by the number on the spinner. These different strategies are shown below for the example 35 ÷ 6 = 5, R5.
STRATEGIES
Strategy Description
Example
Count by the divisor
6, 12, 18, 24, 30, 36
6 × 6 is 36, and that’s too much, so it must be 5, remainder 5.
Repeatedly subtract the divisor
from the dividend
35 – 6 = 29
29 – 6 =23
23 – 6 = 17
17 – 6 = 11
11 – 6 = 5
I can’t take away 6 anymore. So I took away 6 five times, and I have 5 left. So it must
be 5, remainder 5.
Draw an array on the Number
Chart
So, 35 ÷ 6 = 5, R5
6 × 5 = 30
© The Math Learning Center
5 left
Bridges Breakouts
Building Computational Fluency Blackline S 23.2 Run back-to-back with NC S 23.3.
Support Activity 23
SUPPORT ACTIVITY
Remainders Win
You’ll need
H Instructions for Remainders Win (Blacklines NC S 23.2 and 23.3, 1 copy of each run back-toback)
H Divisor Spinner (Blackline S 23.4, 1 copy for each pair of players, cut in half)
H Remainders Win Record Sheet (Blackline S 23.5, 1 copy for each player)
H Array Challenge Cards, pages 1–3 (Blacklines NC S 13.3–13.5, 1 copy cut apart for each pair
of players)
H Number Charts (Blackline S 23.6, 1 copy for each player, optional)
H paper clip and pencil to use as a spinner
Instructions for Remainders Win
1
Take turns spinning the spinner.
The player with the higher number is
Player 1 and the other player is Player
2. Write your names in the correct
places on the record sheet.
2
Mix up the Array Cards and place
them in a stack face down between you.
3
Player 1 draws the first card and
finds the product for the array shown
on the card.
Blackline NC S 23.4 Run 1 copy for each player.
NAME
Cheyenne
DATE
April 12
Remainders Win Record Sheet
PLAYER 1
Cheyenne
PLAYER 2
James
35 x 6 = 5 R5
Blackline NC S 23.3
Divisor Spinner
Remainder Total
9
4
8
7
4
Remainder Total
5
6
Then, Player 1 spins the spinner
and divides the product by the number
on the spinner.
5
Player 1 writes the division equation
in the first box on the record sheet and
circles the remainder if there was one.
Bridges Breakouts
Remainder Total
© The Math Learning Center
Remainder Total
(Continued on back.)
PRE-PUBLICATION DRAFT
Number Corner
© The Math Learning Center
Building Computational Fluency Blackline S 23.3 Run back-to-back with NC S 23.2.
Support Activity 23 (cont.)
6
Now Player 2 follows steps 3–5 to
take a turn.
7
Take turns until each player has
gone 10 times.
8
At the end of the game, both players
add up all their remainders. The player with the highest total wins.
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 23.4 Run 1 copy for every 2 pairs of players. Cut in half and give each pair a spinner.
Divisor Spinner
9
4
8
5
7
6
9
4
Divisor Spinner
8
5
7
Bridges Breakouts
6
© The Math Learning Center
Building Computational Fluency Blackline S 23.5 Run 1 copy for each player.
NAME
DATE
Remainders Win Record Sheet
Player 1
Player 2
Remainder Total
Remainder Total
Remainder Total
Remainder Total
© The Math Learning Center
Bridges Breakouts
Building Computational Fluency Blackline S 23.6 Run 1 copy for each player as needed.
NAME
DATE
Number Charts
Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline F
Fact Fluency Supplement Multiplication and Division
The Fact Fluency Supplement provides the kind of practice students need to become fluent with multiplication and related division facts, and is designed to complement any intermediate grade math
program. You can assess students’ fluency on a regular basis using Assessment 3: Quick Facts (pages
35–39), or you can use the Fact Fluency Supplement as a stand-alone resource if you prefer. The supplement contains a 6-page section for each multiplier from 2 through 12. The material in this supplement
is based on accessible and effective strategies for learning and remembering multiplication and related
division facts. The table below summarizes each for your reference.
MULTIPLICATION STRATEGIES
Factor
Category
Example
How the strategy works
×2
doubles
2 × 6 = 12
9 × 2 = 18
To multiply any number by 2, double that number.
×3
doubles plus 1 set facts
3 × 6 = 18
9 × 3 = 27
To multiply any number by 3, double the number and then add that number.
For example, 3 × 6 = (2 × 6) + 6, which equals 18.
×4
double-doubles
4 × 6 = 24
9 × 4 = 36
To multiply any number by 4, double that number and then double the
result. For example, 4 × 6 = 2(2 × 6). This is equivalent to 2 × 12 = 24.
×5
half-decade facts
5 × 7 = 35
8 × 5 = 40
To multiply any number by 5, multiply by 10 first and divide the result by 2.
For example, 5 × 7 = (10 × 7) ÷ 2. 10 × 7 = 70, and 70 ÷ 2= 35.
×6
triple then double facts
6 × 7 = 42
8 × 6 = 48
To multiply any number by 6, triple the number first and then double the
result. For example, 6 × 7 = 2(3 × 7). 3 × 7 = 21, and 21 × 2 = 42.
×8
double-double-doubles
4 × 8 = 32
8 × 12 = 96
8 × 12 = (2(2(2 × 8))). 2 × 8 = 16, 2 × 16 = 32, and 2 × 32 = 64.
9 × 7 = 63
9 × 9 = 81
To multiply any number by 9, think of the related decade fact and then
subtract 1 set of the number itself. For example, 9 × 7 = (10 × 7) – 7.
×9
decade minus 1 set facts
To multiply any number by 8, double the number 3 times. For example,
(10 × 7) – 7 = 70 – 7, which is 63.
x10
decade facts
10 × 7 = 70
9 × 10 = 90
Multiplying by 10 comes naturally for students who have a solid grasp of
skip counting and place value concepts.
×11
decade plus 1 set facts
11 × 3 = 33
8 × 11 = 88
To multiply any number by 11, think of the related 10’s fact and then add 1
set of the number itself. For example, 11 × 9 = (10 × 9) + 9. (10 × 9) + 9 =
90 + 9, which is 99.
×12
decade plus 2 sets facts
12 × 5 = 60
7 × 12 = 84
To multiply any number by 12, think of the related 10’s fact and then add 2
sets of the number itself. For example, 12 × 7 = (10 × 7) + (2 × 7). (10 × 7)
+ (2 × 7) = 70 + 14, which is 84.
You’ll notice that there is no explicit strategy for multiplying by 7. That’s because all of the 7’s facts, with
the exception of 7 × 7, can be solved using the other strategies. Students will generate their own strategies for 7 × 7, for example, recalling that 7 × 5 is 35 and then adding 7 × 2 for a total of 49. Others may
remember that 7 × 6 is 42 and add another 7 to get 49.
You’ll notice too, that there are no explicit division strategies listed above. This is because students generally learn their division facts by remembering the related multiplication facts. The expression 56 ÷ 7, for
instance, can be interpreted to mean, “How many 7’s are there in 56?” This question is easily answered
if one knows that 8 × 7 = 56. For this reason, every worksheet in this supplement pairs multiplication
and division. In order to provide that extra boost many students need with division, however, this operation is featured on the game sheets throughout the supplement.
© The Math Learning Center
Bridges Breakouts  
Building Computational Fluency Blackline F
Fact Fluency Supplement Multiplication and Division (cont.)
The Fact Fluency Supplement contains a 6-page section for each multiplier from 2 through 12. For each
multiplier, you’ll find” 2 worksheets, 2 games, and a set of flashcards suitable for use at home or school.
These materials are formatted in the same way for every multiplier, and each set refers to a strategy for
multiplying by that number.
Depending on the needs of your class, you might run a copy of the entire supplement for each student
to use throughout the year. Alternatively, you might run multiple copies of the sheets for each multiplier
and each range of facts and keep them in labeled folders that are easily accessible to students. You can
have students work on the packets at school during a designated time and/or take them home for practicing with a family member.
Fact Fluency Packets

Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline F 25
NAME
DATE
Fact Fluency with 6’s Multiplying & Dividing by 6
MULTIPLICATION FACT FLUENCY
Strategy
How It Works
Example
Triple Then Double
To multiply any number by 6,
triple the number and then
double the answer.
What is 6 × 8?
It’s 8 tripled, then doubled.
Triple first: 8 + 8 + 8 = 24
Then double: 24 + 24 = 48
1
Multiply each number in the grid by 6. Write each product in the box. The first
one is done for you.
5
7
3
9
11
8
12
6
2
10
8
11
1
9
5
0
12
4
30
2
Use the triple then double strategy to help solve these combinations.
6 × 15 = ______
25
×6
____
3
6 × 20 = ______
150
×6
____
6 × 33 = ______
6 × 50 = ______
30
×6
____
Use what you know about multiplying by 6 to solve these division problems.
42 ÷ 6 = ______
54 ÷ 6 = ______
36 ÷ 6 = ______
60 ÷ 6 = ______
6 72
6 48
6 66
6 30
© The Math Learning Center
Bridges Breakouts  
Building Computational Fluency Blackline F 26
NAME
DATE
Fact Fluency with 6’s Practice Multiplying by 6 & 5
MULTIPLICATION FACT FLUENCY
1
Circle all the triple then double facts (×6) in blue. Then go back and fill in the
answers with regular pencil.
2
Circle all the half-decade facts (×5) in red. Then go back and fill in the answers with regular pencil.
9
2
6
8
11
7
24
×6
×6
×6
×6
×6
×5
×5
____
____
____
____
____
____
____
3
2
×6
____
5
×6
____
12
×6
____
10
×6
____
9
×6
____
3
×6
____
12
×5
____
4
×6
____
7
×6
____
9
×5
____
11
×5
____
12
×6
____
7
×5
____
12
×6
____
Write two multiplication and two division facts for each set of numbers.
a
b
c
6
8
d
7
6
48
12
72
42
9
6
6
54
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ × ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____
____ ÷ ____ = _____

Bridges Breakouts
© The Math Learning Center
Building Computational Fluency Blackline F 27
NAME
DATE
Fact Fluency with 6’s Division Capture 6’s & 5’s
MULTIPLICATION FACT FLUENCY
4
You’ll need
Try to capture 3 or 4 boxes in a row:
across, up and down, or diagonally.
Keep playing until the gameboard is
filled or neither player can use the number he or she spins 3 times in a row.
H a partner
H 2 pencils or markers in different colors
H paperclip and pencil to use as a spinner
5
1
Then circle the places on the grid
where you got 3 or 4 in a row and add
up your scores.
2
12 3 4
Instructions for Division Capture 6’s & 5’s
Take turns spinning the spinner.
The player who gets the higher number goes first.
Take turns spinning the spinner.
Use the number you spin to fill in the
answer to one of the division problems
below. Be sure to use your own color
pencil.
11
5
10
6
9
3
If the box you need is already filled,
you lose your turn.
15 ÷ 5
50 ÷ 5
60 ÷ 5
36 ÷ 6
7
8
35 ÷ 5
Scoring
48 ÷ 6
20 ÷ 5
18 ÷ 6
55 ÷ 5
54 ÷ 6
72 ÷ 6
40 ÷ 5
60 ÷ 6
30 ÷ 5
24 ÷ 6
42 ÷ 6
25 ÷ 5
45 ÷ 5
30 ÷ 6
66 ÷ 6
© The Math Learning Center
3 in a Row—1 point
4 in a Row—2 points
Player 1
Points
Player 2
Points
Bridges Breakouts  
Building Computational Fluency Blackline F 28
NAME
DATE
Fact Fluency with 6’s Flashcard Bingo 6’s
MULTIPLICATION FACT FLUENCY
2
You’ll need
Take turns pulling 1 card. Each
time, both players color the product on
their board or mark it with an x.
H a partner
H one set of 6’s flashcards and your flashcard pocket
3
H marker or crayon for each player
The first player to get two rows of 4
going horizontally, vertically, or diagonally, wins.
Instructions for Flashcard Bingo 6’s
4
1
Mix up one set of flashcards and arrange them so that the multiplication
side is facing up on all of them. Put
them in the flashcard pocket.
Play the game a second time using
the division side of your cards.
Game 1 ×
Player 1
Player 2
54
30
72
36
24
12
6
30
48
66
12
54
30
66
72
12
36
6
42
60
18
54
60
6
42
24
18
48
42
48
36
18
Game 2 ÷
Player 1

Bridges Breakouts
Player 2
1
6
11
10
3
6
7
4
5
10
9
2
8
11
12
6
12
4
8
12
5
9
10
7
9
11
3
7
1
8
5
2
© The Math Learning Center
Building Computational Fluency Blackline F 29 Run back-to-back with Blackline F 30.
Fact Fluency with 6’s Flashcards, page 1 of 2
•
•
•
•
Cut out this set of 12 flashcards.
Fold a 3-by-5 index card in half.
Tape or staple both sides but leave the top open.
Label this storage pocket with your name and the set number.
1
2
3
4
× 6 ___
× 6 ___
× 6 ___
×6
___
Blackline F 29
Blackline F 29
Blackline F 29
Blackline F 29
5
6
7
8
× 6 ___
× 6 ___
× 6 ___
×6
___
Blackline F 29
Blackline F 29
Blackline F 29
Blackline F 29
9 10 11 12
× 6 ___
× 6 ___
× 6 ___
×6
___
Blackline F 29
© The Math Learning Center
Blackline F 29
Blackline F 29
Blackline F 29
Bridges Breakouts  
Building Computational Fluency Blackline F 30 Run back-to-back with Blackline F 29.
Fact Fluency with 6’s Flashcards, page 2 of 2
24 ÷ 6
Blackline F 30
48 ÷ 6
Blackline F 30
72 ÷ 6
Blackline F 30

Bridges Breakouts
18 ÷ 6
Blackline F 30
42 ÷ 6
Blackline F 30
66 ÷ 6
Blackline F 30
12 ÷ 6
Blackline F 30
36 ÷ 6
Blackline F 30
60 ÷ 6
Blackline F 30
6÷6
Blackline F 30
30 ÷ 6
Blackline F 30
54 ÷ 6
Blackline F 30
© The Math Learning Center